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Thursday, June 20, 2013

We in the quantum gravity groups all over the planet search for a unified framework for general relativity and quantum theory. But I have a peripheral interest also in modifications of general relativity and quantum mechanics since altering one of these two ingredients can change the rules of the game. General relativity and quantum mechanics however work just fine as they are, so there is little need to modify them. In fact, modifications typically render them less appealing to the theoretician, for not to say ugly.

Spontaneous localization models for quantum mechanics are, if you ask me, a particularly ugly modification. In these models, one replaces the collapse upon observation in the Copenhagen interpretation by a large number of little localizations that have the purpose of producing eigenstates upon observation. These localizations that essentially focus the spread of the wave-function are built into the dynamics by some stochastic process, and the rate of collapse depends on the mass of the particles (the higher the mass, the higher the localization rate). The purpose of these models is to explain why we measure the effects of superposition, but never a superposition itself, and never experience macroscopic objects in superpositions.

Unfortunately, I have no reason to believe that nature gives a damn what I find ugly or not, and quite possibly you don’t care either. And so, as a phenomenologist, the relevant question that remains is whether spontaneous localization models are a description of nature that agrees with observation.

And, to be fair, on that account spontaneous localization models are actually quite appealing. That is because their effects, or the parameters of the model respectively, can be bounded both from above and below. The reason is that the collapse processes have to be efficient enough to produce eigenstates upon observation, but not so efficient as to wash out the effects of quantum superpositions that we observe.

The former bound on the efficient production of observable eigenstates becomes ambiguous however if you allow for a many worlds interpretation because then you don’t have to be bothered by macroscopic superpositions. Alas, the intersection of the groups of many worlds believers and spontaneous localization believers is an empty set. Therefore, the spontaneous localization approach has a range of parameters with macroscopic superpositions that is “philosophically unsatisfactory,” as Feldman and Tumulka put it in their (very readable) paper (arXiv:1109.6579). In other words, if you allow for a many worlds situation whose main feature is the absence of collapse, then there really is no point to add stochastic localization on top of that. So it’s either-or, and thus requiring absence of macroscopic superpositions bounds possible parameters.

Still, the notion of what constitutes “macroscopic reality” is quite fuzzy. Just to give you an idea of the problem, the estimates by Feldman and Tumulka go along such lines:

“To obtain quantitative estimates for the values [of the model parameters] that define the boundary of the [philosophically unsatisfactory region], we ask under which conditions measurement outcomes can be read off unambiguously... For definiteness, we think of the outcome as a number printed on a sheet of paper; we estimate that a single digit, printed (say) in 11-point font size, consists of 3 x 1017 carbon atoms or N = 4 x 1018 nucleons. Footnote 1: Here is how this estimate was obtained: We counted that a typical page (from the Physical Review) without figures or formulas contains 6,000 characters and measured that a toner cartridge for a Hewlett Packard laser printer weighs 2.34 kg when full and 1.54 kg when empty. According to the manufacturer, a cartridge suffices for printing 2 x 104 pages...”

And so on. They also discuss the question whether chairs exist:

“One could argue that the theory actually becomes empirically refuted, as it predicts the nonexistence of chairs while we are sure that chairs exist in our world. However, this empirical refutation can never be conclusively demonstrated because the theory would still make reasonable predictions for the outcomes of all experiments...”

Meanwhile on planet earth, particle physicists calculate next-to-next-to-next-to leading order corrections to the Higgs cross-section.

Sarcasm aside, my main problem with this, and with most interpretations and modifications of quantum mechanics, is that we already know that quantum mechanics is not fundamentally the correct description of nature. That’s why we teach 2nd quantization to students. To make matters worse, most of such modifications of quantum mechanics deal with the non-relativistic limit only. I thus have a hard time getting excited about collapse models. But I’m digressing - we were discussing their phenomenological viability.

In fact, Feldman and Tumulka’s summary of experimental (ie non-philosophic) constraints isn’t quite as mind-enhancing as the nonexistent chair I’m sitting on. (Hard science, my ass.) Some experimental constraints they are discussing: The stochastic process of these models contributes to global warming by injecting energy with each collapse and since there’s some cave in Germany which doesn’t noticeably warm up in July, this gives a constraint. And since we have not heard any “spontaneous bangs” around us that would accompany the collapses in certain parameter ranges, we get another constraint. Then there’s atom interferometry. And then there’s this very interesting recent paper

For spontaneous localization the effect scales differently with the mass though, and is thus not testable in neutral Kaon oscillation. Since the localization effects get larger with large masses, the authors recommend to instead look for the effects of collapse models in chiral molecules.

Chiral molecules are pairs of molecules with the same atomic composition but with a different spatial arrangement. And some of these molecules can exist in superpositions of such spatial arrangements that can transform into each other. In the small temperature limit, this leads to an observable level splitting in the molecular spectrum. The best known example may be ammonia.

Now if collapse models were correct, then these spatial superpositions of chiral molecules should localize and the level splitting, which is a consequence of superpositions of two eigenstates, become unobservable. The authors estimate that with current measurement precision the bound from molecular level splitting is about comparable to that of atom interferometry (where interference should become unobservable if spontaneous localization is too efficient, thus leading to a bound). Molecular spectroscopy is a presently very active research area and with better resolution and larger molecules, this bound could be improved.

In summary, this nice paper gives me hope that in the soon future we can put the ugly idea of spontaneous localization to rest.

Regarding Penrose - I have some sympathy for the idea, but I'm unenthusiastic about it for the same reasons I mentioned above. I'd like to see how it's compatible with quantum field theory and its symmetries. Now I totally understand that if one proposes an idea then there will be details missing and it takes some while to work this out, but there doesn't seem to be much progress on that account, at least I haven't seen anything. This is not to say that I think it's impossible to make it work. Best,

Hello Bee,there are two errors in re wording in that sentence.A molecule is a molecule, not a pair of molecules. Chiral molecules together with their enantomeric counterpart make a enantiomeric pair.

""...with the same atomic composition but with a different spatial arrangement.""This definition includes all isomers,like butane vs isobutane, pentane vs neopentane.The shortest definition for a chiral molecule is a molecule lacking any symmetry operation, I think.The molecule to look for the effects mentioned might be ethylmethylamine.Problem is, that any substituent (replacing one of the hydrogens of ammonia) will lower the barrier between the "inverted umbrella" structures.If the height of the barrier gets lower than lowest vibrational level, all theeffects of ammonia masers will vanish.RegardsGeorg

The interpretation issues of quantum theory are a very interesting domain, but unfortunately it also suffers from "religious wars".

My personal stance is that in as far as:- one thinks of quantum theory as a fundamental theory of nature (describing ontology)- one considers that there is some sort of an objective reality (that has to be described by a fundamental theory)

...then there is no escape but to resort to some or other version of MWI because the fundamental principles of QM are unitarity and the superposition principle.

The only ways of escaping this are by assuming that:

- there is no objective reality, or that objective reality is not ontologically described by quantum theory - this is essentially the Copenhagen version, which oscillates somewhat between both viewpoints. Quantum theory is then just a calculation tool that helps us find out probabilities of events, but the mathematical structures used in these calculations are then not in relationship with "reality" (because that reality doesn't exist, because it is of a different nature than the mathematical structure of QM, or because it cannot be described by mathematical entities for one or other unstatable reason)

- quantum theory is only approximately true and von Neumann's process 1 and 2 are limiting cases for the "true" process. This is what these spontaneous localization processes postulate.

However, concerning the philosophically uncomfortable zone where you have to consider that things you can "macroscopically observe" have to reside in superposition, I have 2 remarks.

The first is that no spontaneous localization process will be able to resolve the so-called Bell/Aspect/EPR like issues unless they really screw up Lorentz invariance in principle. You can indeed scale up any Aspect-like experiment to such an extend that a whole book is printed on the Alice side, and on the Bob side, depending on the outcomes, before the light cones of both observations cross, by increasing the distance between Alice and Bob sufficiently (say, one on Jupiter and one on Earth).Any truly physical collapse process that allows for a violation of the Bell limits must then have books in superpositions, or propagate the local collapse faster than light.

The other remark is that in as much as observers are also quantum systems, there is absolutely no difficulty with the fact that we can't see any macroscopic system "in superposition" while we would objectively be in superposition.

The point is that in as much as we keep the illusion of free will, it is impossible for us to experience two "branches" simultaneously, because otherwise we could "decide" to act in one branch using the observation in the other, which would be not only a violation of unitarity, but even of linearity, and screw the superposition principle.

Let me elaborate.

Image that you look at a green or red LED light. After that interaction, your body is in the following state:

|you_green) |greenLED) + |you_red) |redLED)

Now, imagine that "you" as a conscious entity can experience your two bodystates at the same time, that you are aware of you_green as well as you_red.

You could "decide" that if you are aware of the TWO states, you push the yellow button, while if you are aware of only ONE state, you push the black button.

Well, the above state would evolve into:

|you_green) |greenLED)|yellow) + |you_red) |redLED)|yellow)

if you were aware of both states.

However, the state

|you_green) |greenLED) alone would evolve into:

|you_green) |greenLED)|black)

and you see that linearity is gone.

So it is impossible, even if you are as an observer in a superposition, to be aware of that superposition and to have the illuseion of free will.

Yes, you are right, it's a very sloppy sentence, sorry. I meant to link to this earlier post for details, but then evidently forgot about it. I'll take a mental note that some readers are reading closely and that there's no excuse for sloppiness :o) Best,

I am very confused about the problem many physicists have with the collapse of superposition states after measurement. Either there is something I fundamentally do not get that makes it seem intuitive to me, or there is something they do not fundamentally get that makes it not intuitive to them.

The field is the fundamental measurable quantity in physics. Even though you can't see it, it still exists. In order to "see" it you must measure it via a probe of some sort. The field has an objective reality that includes our own existance because we are in the field if we get close enough to measure it.

As you localize the measurement to smaller and smaller points in that field tbe measurement is subject to larger and larger turbulence effects due to the energy required to make the measurement.

An example in the macroscopic world would be a simple wind anemometer. As long as you measure in a large open area you will get an accurate reading. The annemometer itself will have an insignificant effect on the direction and intensity of the wind.

But if you put that same anemometer in a narrow tunnel only twice the diameter of the instrument then the probability will be that the wind will just chose to take a path on either side of the anemometer and leave the anemometer stalled. You can't say that there were two objective realities before this occurs. There was ALWAYS just one objective value for the vector field at various times but the energy used to measure it, the mass of the anemometer in this case, altered that invisible field.

Hello Bee, ammonia with three different hydrogen isotopes, "NHDT" is a better molecule to look for the effects of optical isomers.A magnetic field on top of the electric quadrupole field in the maser will do the separation of enantiomers, if necessary.RegardsGeorg

Patrick Van Esch said " You can indeed scale up any Aspect-like experiment to such an extend that ..."

Actually, that's not at all obvious. Nobody knows enough about physics yet to know how to scale it up that far. So it's not obvious such a scaled-up experiment would even be possible, let alone produce the expected result.

The problem with MWI is that it doesn't answer the basic question: Why, and how, is one component of the state observed but another isn't?

Experiments in physics have always been about making observations and then trying to describe and explain the observables, in the faith that they tell us something about reality. But MWI brushes away observables as mere tricks of the mind. It takes unitarity and linearity as exact axioms, and excuses away everything, even reality itself, that indicates otherwise.

@Georg: "The shortest definition for a chiral molecule is a molecule lacking any symmetry operation, I think." A 3-D chiral point assemblage or body contains no S_n symmetries (improper rotations, rotation-reflection axes. A baseball’s seam has S_4 symmetry). Rotation symmetries are irrelevant, e.g., point groups T (but not T_h or T_d), O, I. The hierarchy is helicity (depends on point of view unless relativistic), chirality (invert one coordinate axis to obtain non-superposable mirror images), then parity (invert all coordinate axes to give a non-superposable pair, inside-out and upside-down).

Parity is an absolute discontinuous symmetry. Noether’s theorems arising through Lie groups cannot touch it. The center of mass of the molecule may not change position during inversion, , for that would be translation. For NH_3, hydrogens are light. How ‘bout for NF_3?

I agree with Collin about MWI. One can be smart in physics but not wise.

To add further elaboration to my earlier argument about there really being only one objective reality both before and after measurement: If you poll a population of people with questions in a very restricted "yes/no" manner and frame the questions very narrowly it will have ramifications. For instance, one can frame a question in such a way that if a person is forced to answer yes/no then he or she will give an answer that is might seem out of character with that person. You could interpret the result of the poll as have a population that is very radical and polarized when in fact they are not at all.

In fact nothing has changed except the force of the question put them in a box. There is really nothing at all different in principle from what is going on in quantum physics. If an action is later required of the population or individuals based on many different issues that person or group will return to their prior disposition as if nothing had ever changed. In fact nothing DID change. The force of the question in the poll temporarily put the individuals in a radical position.

I think scientists, if they really want to capture the publics imagination, should just stop with all the sci fi speculation and relate basic principles of science to real life. Now that would be a guiding principle for life that most people could get behind.